两弹性接触粗糙快速滑动表面温升的分形模型

采用球形微凸体的赫兹接触理论和MB模型,对微接触点的温升进行了分析,得到了快速滑动区域内的分形区域实际接触面积的温升概率分布密度、温升补充累积概率分布函数的封闭式表达式.分析结果说明:量纲一特定滑动区域的实际接触面积随量纲一最大Jaeger参数增加而单调减小.量纲一最大温升随分形维数增加而减小,但随分形粗糙度参数增加而增加.量纲一温升随分形维数增加而增加.当分形维数为1.5时,实际接触面积的温升概率分布密度等于在一个弹性微接触点面积上的温升概率分布密度,基于正八边形面积的近似解适当接近精确解.温升的补充累积概率分布函数随分形维数、滑动速度和量纲一分形粗糙度参数增加而增加.

Fractal Model of Temperature Rise between Two Elastic Contact Rough Fast Sliding Surfaces

The microcontact temperature rises were analyzed in light of the Hertz contact theory for spherical asperity tips and Majumdar-Bhushan model.The closed form expressions for the probability distribution density and complementary cumulative probability distribution function of the temperature rise at the real contact area of a fractal domain were deduced for the fast sliding region.The analytical results indicate that the dimensionless real contact areas in specified sliding regions monotonically decrease with increasing dimensionless maximum Jaeger parameter.The dimensionless maximum temperature rise decreases with increasing fractal dimension;while it increases with increasing fractal roughness parameter.The dimensionless temperature rise increases with increasing fractal dimension.When the fractal dimension equals 1.5,the probability distribution density of temperature rise at the real contact area is identical to that of temperature rise at an elastic microcontact area;and the approximate solutions based on the normal octagonal area is reasonably close to the exact solution.The complementary cumulative probability distribution function of the temperature rise increases with all increasing fractal dimension,sliding velocity and dimensionless fractal roughness parameter.